It has been suggested by Y. Meyer and numerically confirmed by many others that dual spaces are good for texture recovery. Among the dual spaces, our work focuses on Sobolev spaces of negative differentiability to recover texture from noisy blurred images. Such Sobolev spaces are good to model oscillatory component, on the other hand, the spaces themselves hardly distinguishes texture component from noise component because noise is also considered to be a highly oscillatory component. In this talk, in addition to oscillatory component recovery, we will further investigate a one-parameter family of Sobolev norms to achieve such a separation task.